Asymptotic Analysis - Volume 106, issue 3-4

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ISSN 0921-7134 (P)
ISSN 1875-8576 (E)

Impact Factor 2018: 0.748

The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand.

Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.

Abstract: We study the location of the transmission eigenvalues in the isotropic case when the restrictions of the refraction indices on the boundary coincide. Under some natural conditions we show that there exist parabolic transmission eigenvalue-free regions.

Abstract: In this paper, we consider the dynamics of multi-valued processes generated by nonautonomous lattice systems with delays. In particular, the effects of small delays on the asymptotic behavior of multi-valued nonautonomous lattice systems and finite lattice approximation of infinite delay lattice systems are presented. We do not assume any Lipschitiz condition on the nonlinear term, just a continuity assumption together with growth condition, so that uniqueness of solutions of the problem fails to be true.

Abstract: In this paper, we consider a mean field game (MFG) model perturbed by small common noise. Our goal is to give an approximation of the Nash equilibrium strategy of this game using a solution from the original no common noise MFG whose solution can be obtained through a coupled system of partial differential equations. We characterize the first order approximation via linear mean-field forward-backward stochastic differential equations whose solution is a centered Gaussian process with respect to the common noise. The first order approximate strategy can be described as follows: at time t ∈ [ 0 , T ]…, applying the original MFG optimal strategy for a sub game over [ t , T ] with the initial being the current state and distribution. We then show that this strategy gives an approximate Nash equilibrium of order ϵ 2 .
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